What stakes? If it's 20-40 minutes, the worst that can happen is that you might miss your flight. It sounds like BAA/BA have plans in place to minimise the chances of even that, particularly if missing the flight might cause real disruption to your journey.
The stakes for the airline = quite a bit of disruption and cost, the stake for the passenger, well who knows, what if it is someone rushing to hospital to see a loved one in their final hours?
Don't have much empathy, do you?